def test_compute_irasa(tsig_comb):
# Estimate periodic and aperiodic components with IRASA
f_range = [1, 30]
freqs, psd_ap, psd_pe = compute_irasa(tsig_comb, FS, f_range, noverlap=int(2*FS))
assert len(freqs) == len(psd_ap) == len(psd_pe)
# Compute r-squared for the full model, comparing to a standard power spectrum
_, powers = trim_spectrum(*compute_spectrum(tsig_comb, FS, nperseg=int(4*FS)), f_range)
r_sq = np.corrcoef(np.array([powers, psd_ap+psd_pe]))[0][1]
assert r_sq > .95
def build_all(sig, fs, n_build=np.inf, sleep=0.05, label='viz', save=False):
"""Build all plots together."""
size = 750
step = 2
start = 2000
sig_yielder = yield_sig(sig, start=start, size=size, step=step)
for ind in range(n_build):
clear_output(wait=True)
fig, axes = make_axes()
spect_sig = sig[start + step * ind - 2000:start + step * ind + 2000]
freqs, powers = trim_spectrum(*compute_spectrum(spect_sig, fs=fs),
[1, 50])
plot_timeseries(next(sig_yielder), ax=axes[0])
plot_spectra(freqs, powers, log_freqs=True, ax=axes[1])
animate_plot(fig, save, ind, label=label, sleep=sleep)
def compute_irasa(sig, fs=None, f_range=(1, 30), hset=None, **spectrum_kwargs):
"""Separate the aperiodic and periodic components using the IRASA method.
Parameters
----------
sig : 1d array
Time series.
fs : float
The sampling frequency of sig.
f_range : tuple or None
Frequency range.
hset : 1d array
Resampling factors used in IRASA calculation.
If not provided, defaults to values from 1.1 to 1.9 with an increment of 0.05.
spectrum_kwargs : dict
Optional keywords arguments that are passed to `compute_spectrum`.
Returns
-------
freqs : 1d array
Frequency vector.
psd_aperiodic : 1d array
The aperiodic component of the power spectrum.
psd_periodic : 1d array
The periodic component of the power spectrum.
Notes
-----
Irregular-Resampling Auto-Spectral Analysis (IRASA) is described in Wen & Liu (2016).
Briefly, it aims to separate 1/f and periodic components by resampling time series, and
computing power spectra, effectively averaging away any activity that is frequency specific.
References
----------
Wen, H., & Liu, Z. (2016). Separating Fractal and Oscillatory Components in the Power Spectrum
of Neurophysiological Signal. Brain Topography, 29(1), 13–26. DOI: 10.1007/s10548-015-0448-0
"""
# Check & get the resampling factors, with rounding to avoid floating point precision errors
hset = np.arange(1.1, 1.95, 0.05) if not hset else hset
hset = np.round(hset, 4)
# The `nperseg` input needs to be set to lock in the size of the FFT's
if 'nperseg' not in spectrum_kwargs:
spectrum_kwargs['nperseg'] = int(4 * fs)
# Calculate the original spectrum across the whole signal
freqs, psd = compute_spectrum(sig, fs, **spectrum_kwargs)
# Do the IRASA resampling procedure
psds = np.zeros((len(hset), *psd.shape))
for ind, h_val in enumerate(hset):
# Get the up-sampling / down-sampling (h, 1/h) factors as integers
rat = fractions.Fraction(str(h_val))
up, dn = rat.numerator, rat.denominator
# Resample signal
sig_up = signal.resample_poly(sig, up, dn, axis=-1)
sig_dn = signal.resample_poly(sig, dn, up, axis=-1)
# Calculate the power spectrum using the same params as original
freqs_up, psd_up = compute_spectrum(sig_up, h_val * fs,
**spectrum_kwargs)
freqs_dn, psd_dn = compute_spectrum(sig_dn, fs / h_val,
**spectrum_kwargs)
# Geometric mean of h and 1/h
psds[ind, :] = np.sqrt(psd_up * psd_dn)
# Now we take the median resampled spectra, as an estimate of the aperiodic component
psd_aperiodic = np.median(psds, axis=0)
# Subtract aperiodic from original, to get the periodic component
psd_periodic = psd - psd_aperiodic
# Restrict spectrum to requested range
if f_range:
psds = np.array([psd_aperiodic, psd_periodic])
freqs, (psd_aperiodic,
psd_periodic) = trim_spectrum(freqs, psds, f_range)
return freqs, psd_aperiodic, psd_periodic
# Plot a segment of the extracted time series data plot_time_series(times, sig) ################################################################################################### # Calculate Power Spectra # ----------------------- # # Next lets check the data in the frequency domain, calculating a power spectrum # with the median welch's procedure from NeuroDSP. # ################################################################################################### # Calculate the power spectrum, using a median welch & extract a frequency range of interest freqs, powers = compute_spectrum(sig, fs, method='welch', avg_type='median') freqs, powers = trim_spectrum(freqs, powers, [3, 30]) ################################################################################################### # Check where the peak power is peak_cf = freqs[np.argmax(powers)] print(peak_cf) ################################################################################################### # Plot the power spectra, and note the peak power plot_power_spectra(freqs, powers) plt.plot(freqs[np.argmax(powers)], np.max(powers), '.r', ms=12) ################################################################################################### # Look for Bursts
def compute_irasa(sig,
fs,
f_range=None,
hset=None,
thresh=None,
**spectrum_kwargs):
"""Separate aperiodic and periodic components using IRASA.
Parameters
----------
sig : 1d array
Time series.
fs : float
The sampling frequency of sig.
f_range : tuple, optional
Frequency range to restrict the analysis to.
hset : 1d array, optional
Resampling factors used in IRASA calculation.
If not provided, defaults to values from 1.1 to 1.9 with an increment of 0.05.
thresh : float, optional
A relative threshold to apply when separating out periodic components.
The threshold is defined in terms of standard deviations of the original spectrum.
spectrum_kwargs : dict
Optional keywords arguments that are passed to `compute_spectrum`.
Returns
-------
freqs : 1d array
Frequency vector.
psd_aperiodic : 1d array
The aperiodic component of the power spectrum.
psd_periodic : 1d array
The periodic component of the power spectrum.
Notes
-----
Irregular-Resampling Auto-Spectral Analysis (IRASA) is an algorithm ([1]_) that aims to
separate 1/f and periodic components by resampling time series and computing power spectra,
averaging away any activity that is frequency specific to isolate the aperiodic component.
References
----------
.. [1] Wen, H., & Liu, Z. (2016). Separating Fractal and Oscillatory Components in
the Power Spectrum of Neurophysiological Signal. Brain Topography, 29(1), 13–26.
DOI: https://doi.org/10.1007/s10548-015-0448-0
"""
# Check & get the resampling factors, with rounding to avoid floating point precision errors
hset = np.arange(1.1, 1.95, 0.05) if hset is None else hset
hset = np.round(hset, 4)
# The `nperseg` input needs to be set to lock in the size of the FFT's
if 'nperseg' not in spectrum_kwargs:
spectrum_kwargs['nperseg'] = int(4 * fs)
# Calculate the original spectrum across the whole signal
freqs, psd = compute_spectrum(sig, fs, **spectrum_kwargs)
# Do the IRASA resampling procedure
psds = np.zeros((len(hset), *psd.shape))
for ind, h_val in enumerate(hset):
# Get the up-sampling / down-sampling (h, 1/h) factors as integers
rat = fractions.Fraction(str(h_val))
up, dn = rat.numerator, rat.denominator
# Resample signal
sig_up = signal.resample_poly(sig, up, dn, axis=-1)
sig_dn = signal.resample_poly(sig, dn, up, axis=-1)
# Calculate the power spectrum, using the same params as original
freqs_up, psd_up = compute_spectrum(sig_up, h_val * fs,
**spectrum_kwargs)
freqs_dn, psd_dn = compute_spectrum(sig_dn, fs / h_val,
**spectrum_kwargs)
# Calculate the geometric mean of h and 1/h
psds[ind, :] = np.sqrt(psd_up * psd_dn)
# Take the median resampled spectra, as an estimate of the aperiodic component
psd_aperiodic = np.median(psds, axis=0)
# Subtract aperiodic from original, to get the periodic component
psd_periodic = psd - psd_aperiodic
# Apply a relative threshold for tuning which activity is labeled as periodic
if thresh is not None:
sub_thresh = np.where(
psd_periodic - psd_aperiodic < thresh * np.std(psd))[0]
psd_periodic[sub_thresh] = 0
psd_aperiodic[sub_thresh] = psd[sub_thresh]
# Restrict spectrum to requested range
if f_range:
psds = np.array([psd_aperiodic, psd_periodic])
freqs, (psd_aperiodic,
psd_periodic) = trim_spectrum(freqs, psds, f_range)
return freqs, psd_aperiodic, psd_periodic
} } # Define the frequency range of interest for the analysis f_range = (1, 40) # Create the simulate time series sig = sim_combined(n_seconds, fs, components) ################################################################################################### # Compute the power spectrum of the simulated signal freqs, psd = compute_spectrum(sig, fs, nperseg=4 * fs) # Trim the power spectrum to the frequency range of interest freqs, psd = trim_spectrum(freqs, psd, f_range) # Plot the computed power spectrum plot_power_spectra(freqs, psd, title="Original Spectrum") ################################################################################################### # # In the above spectrum, we can see a pattern of power across all frequencies, which reflects # the 1/f activity, as well as a peak at 10 Hz, which represents the simulated oscillation. # ################################################################################################### # IRASA # ----- # # In the analysis of neural data, we may want to separate aperiodic and periodic components